Exam 18: A Macroscopic Description of Matter

A weather balloon contains 12.0 m³ of hydrogen gas when the balloon is released from a location at which the temperature is 22.0°C and the pressure is 101 kPa. The balloon rises to a location where the temperature is -30.0°C and the pressure is 20.0 kPa. If the balloon is free to expand so that the pressure of the gas inside is equal to the ambient pressure, what is the new volume of the balloon? Assume that in both cases the hydrogen gas is in thermal equilibrium with the outside air.

The coefficient of volume expansion of olive oil is 0.68 × 10^-3 K^-1. A 1.00-L glass beaker is filled to the brim with olive oil at room temperature. The beaker is placed on a range and the temperature of the oil and beaker increases by 25°C. As a result, 0.0167 L of olive oil spill over the top of the beaker. What is the coefficient of linear expansion of the glass?

Sometimes an experiment requires a certain pure gas to be used at reduced pressure. One way to achieve this is to purchase a sealed glass container filled with the gas, and to introduce the gas into a vacuum by attaching the glass container to the vacuum chamber and breaking the tip of the glass container using a metallic bean and a magnet. If the volume of the glass container is 1.0 L and it is at a pressure of 1.0 × 10⁵ Pa and if the vacuum chamber has a volume of 2.0 L, what will the pressure be after the gas, which is to be assumed to be an ideal gas, is released into the vacuum chamber and the temperature has returned to its original value? (Note that the glass container remains part of the system.)

A cold trap is set up to cause molecules to linger near the suction in a vacuum system. If the cold trap has an effective volume of 0.200 L and is maintained at how many molecules are in it at 10.0 Pa of pressure? (Avogadro's number is 6.022 × 10²³ molecules/mol, and the universal gas constant is 8.314 J/mol ∙ K. Assume the behavior of an ideal gas.)

A rod has a length 2.00000 m at 10.0°C. The length of the rod increases to 2.00060 m when the temperature increases to 30.0°C. What is the coefficient of linear expansion of the material from which the rod is made?

The interior of a refrigerator has a volume of 0.600 m³. The temperature inside the refrigerator in 282 K, and the pressure is 101 kPa. If the molecular weight of air is 29 g/mol, what is the mass of air inside the refrigerator? The ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K.